Semi-partitioned scheduling algorithms attempt to utilize the spare capacity in the partitioned approaches by splitting a number of tasks between processors. The main challenge in these approaches is how to split tasks and assign each partition to a different processor to achieve the highest system utilization while the lowest number of processors is employed. Besides, these schemes must guarantee the schedulability of the real-time tasks. To schedule sporadic real-time tasks on the multi-core systems, we presented a new semi-partitioned algorithm. The algorithm is based on the Rate-Monotonic Scheduling (RMS) policy and can successfully schedule any task sets with the system utilization up to the Liu&Layland bound per each processor. Our extensive experiment results demonstrate that the proposed algorithm can significantly improve the scheduling performance compared with previous work in terms of system utilization and the number of required processors.